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arXiv · 1409.3874

Shock Formation in Lovelock Theories

Harvey S. Reall·Norihiro Tanahashi·Benson Way
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Abstract

We argue that Lovelock theories of gravity suffer from shock formation, unlike General Relativity. We consider the propagation of (i) a discontinuity in curvature, and (ii) weak, high frequency, gravitational waves. Such disturbances propagate along characteristic hypersurfaces of a "background" spacetime and their amplitude is governed by a transport equation. In GR the transport equation is linear. In Lovelock theories, it is nonlinear and its solutions can blow up, corresponding to the formation of a shock. We show that this effect is absent in some simple cases e.g. a flat background spacetime, and demonstrate its presence for a plane wave background. We comment on weak cosmic censorship, the evolution of shocks, and the nonlinear stability of Minkowski spacetime, in Lovelock theories.

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Harvey S. Reall, Norihiro Tanahashi, Benson Way. 2014-09-12. Shock Formation in Lovelock Theories. https://doi.org/10.1103/physrevd.91.044013

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